These two words are homonyms. Homonyms are two words that sound the same, but mean two different things.
It's really easy to mix these two up, since their spelling is only different by one letter!
Stationary = (adjective) unmoving, fixed, unchanging, standing still, remaining in one place.
Alice remained stationary until the teacher told her she could take her seat.
Stationery = (noun) writing paper, office supplies
We received beautiful stationery with our names printed on it, as a wedding present.
A Memory Trick:
Stationary (with an a) can imply "standing still". Think: stationary = standing.
The meanings are similar, and the spelling of "standing" is easier to quickly recall.
Or, jot down the two on some stationery, every time you forget!